Summary

Do not consider associativity of prefix minus or (alternative formulation) let prefix minus bind a bit stronger than infix minus.

Pro:

Compatible with current state (fewer programs are rejected)

fewer cryptic rejection messages involving prefix minus

Cons:

Does not explain why and how certain terms are resolved (if they are accepted)

Description

As described in NegationBindsTightly ghc rejects some terms
that are accepted by Hugs and Helium and should not be rejected in general.
However, making negation bind more tightly is not the proposed solution here, because
it would (in my eyes) wrongly resolve "- x ^ 2" to "(-1) ^ 2".

Only operators to the right of prefix negation need to be considered for resolution.

This condition ensures that "4 * -5" is not rejected (as ghc does).

Prefix minus should bind less tight than multiplication but ...

.. (slightly) stronger than addition and subtraction.

The latter condition ensures that "- x # ..." is resolved as "(- x) # ..." for any operator # with lower precedence than multiplication.

"-4 * 5" will be resolved to "-(4 * 5)" as Hugs correctly does already.
I don't know how Helium resolves this, but it does (usually) not matter for multiplication if it were resolved to "(-4) * 5".

However, Hugs rejects "-4 # 5" for a non-left-associative operator # with precedence 6, because it compares associativities for operators with the same precedence. Therefore prefix minus should have a (slightly) higher precedence than infix operators with the precedence of infix minus.

infix # 6
(#) = (-)
x7 = - 4 # 5

x7 are currently rejected by Hugs and ghc. Two solutions are possible. Since "-" should just bind weaker than multiplication the possibility "-(4 # 5)" cannot be justified, thus "(-4) # 5" should be the unique solution.

Surely, one can always disallow "confusing" resolutions, but if we reject "- 4 # 5", we can also reject "- 4 - 5" or "- 4 ^ 5".
Associativity seems wrong to consider for the unary minus function. (But it is an option to simple use the way of Hugs for ghc, too.)

As a further option it is possible to support multiple prefix minus application. ("4 * - - 5" can be resolved in the same way as
"4 * - 5" is).

References

Mixfix analysis [Aasa95] usually only considers the top-level operators of argument terms.
This backs my point 1. above: Do not look to the left of prefix minus, because there is no argument of prefix minus.

Also Isabelle (​http://isabelle.in.tum.de/) allows prefix operators to have lower precedence than infix operators.
Other specification languages (like HasCASL) do so, too. For instance the logical prefix negation binds stronger than logical connectives but weaker than infix equality or other comparisons. (This does not apply to the "not" in Haskell, because "not" is a plain function, no operator).

My point 3. is backed by the fact that "in case of doubt" prefix application should bind stronger than infix application.

replace:
"The handling of the prefix negation operator, -, complicates matters only slightly. Recall that prefix negation has the same fixity as infix negation: left-associative with precedence 6. The operator to the left of -, if there is one, must have precedence lower than 6 for the expression to be legal. The negation operator itself may left-associate with operators of the same fixity (e.g. +). So for example -a + b is legal and resolves as (-a) + b, but a + -b is illegal."

with:
"The handling of the prefix negation operator, -, complicates matters only slightly. (Recall that) prefix negation has lower precedence than infix multiplication. So -a * b resolves as -(a * b) or more importantly -a ^ b as -(a ^ b). Generally, prefix negation extends as long to the right as there are consecutive infix operators with precedences at least as high as multiplication.
The operator to the left of prefix -, if there is one, is ignored. So a + -b or a * -b are legal. Prefix negation binds tighter with infix operators to the right of lower precedence than multiplication. So for example -a + b is legal and resolves as (-a) + b."